A Study of Uncertainties in GPM/DPR Rain Estimates Caused by DSD Parameterization

A Ku- and Ka-band dual-frequency radar (DPR) will soon be flown on the Global Precipitation Measurement (GPM) satellite, and will play a crucial role in mapping precipitation globally. In principle, a dual-frequency radar derives rain rate by estimating the raindrop size distributions (DSD). The DSD is often described by an analytical model, such as the exponential or gamma distribution, with two or three unknown parameters. However, the inability of the modeled DSD to represent actual DSD spectra as well as intrinsic variations of DSD in time and space lead to uncertainties in the estimates of rainfall rate obtained from the radar. Understanding the uncertainties in rain rate estimation that depend on the DSD parameterization is important in evaluating the overall performance of radar rain-retrieval algorithms. DSD parameterization models will have an impact not only on the radar reflectivity rain rate relationship but also on attenuation corrections that are needed to compensate for the loss of the radar signal caused by rain and other hydrometeors. As such, accurate attenuation correction is also an essential component in the DPR algorithms.

In this study, we will first employ measured DSD data taken from a variety of storm systems to create the radar reflectivity factors at Ku- and Ka-band. The generated radar reflectivities are then used to estimate the DSD parameters for a given DSD model according to a particular dual-wavelength technique. Dual-frequency radar techniques usually make use of the differential frequency ratio, defined as the difference of radar reflectivities in decibels between two frequencies, as well as the radar reflectivity at the lower frequency to first infer the DSD parameters and from them the rain rate. The rain rates estimated from the radar-derived DSD will be compared with those directly obtained from the measured DSD spectra. Note that the rain rates derived from the measured DSD serve as the truth. Thus, the difference between the rain rate retrieved by radar and directly measured rain rate can be regarded as the uncertainties in the radar rain estimation related to the DSD parameterization and the inherent errors in the method. To assess the impact of the uncertainties associated with the DSD parameterizations on the overall performance of the DPR rain-retrieval algorithms, we will provide statistical results of the uncertainties in terms of storm types and rain intensity as well as DSD models. Because the simulated reflectivities are directly computed from the measured DSD spectra, they are true or un-attenuated radar reflectivity factors, As such, there is no attenuation correction involved in the procedures described above.

In the second part of our study, we investigate uncertainties in the radar rain retrievals caused by attenuation effects. To construct more realistic vertical radar profiles, a melting layer model is used to describe attenuation in the mixed-phase region. Measured DSDs are used to generate vertical profiles of the equivalent water content and rain rate in the rain and, with suitable modifications to the DSD, in the mixed phase and snow layers. From these inputs, the simulated (both attenuated and un-attenuated) reflectivity profiles at any frequency can be computed. Several dual-wavelength radar profiling algorithms, such as forward and backward approaches as well as some iterative methods, will be tested with the simulated reflectivity profiles for the retrieval of the DSD and rain rates. The retrieved results will be compared against the original DSD and rain data that are used to produce apparent Ku- and Ka-band radar profiles. To test different storm systems, vertical profiles are created with the perfectly-correlated, partially-correlated and totally-uncorrelated DSDs along a vertical column.

The DSD measurement data used in this study are primarily those collected by a series of distrometers during the MC3E field campaign from April to May in 2011 in south-central Oklahoma. The MC3E was sponsored by NASA GPM and ARM programs.